Stretch the tarp over the hole preferably over the ridgeline.
Fix a leaking roof in winter.
Start low soaking the area just above where the leak appears in the house.
Isolate areas when you run the hose.
The secret to caulking in winter time is to heat the sealant in the tube.
Patch the nail or screw holes by slipping a piece of roof flashing underneath the shingle.
Push the shingle or plywood into the tar and trowel more roofing tar around the edges of the patch.
For example soak the downhill side of a chimney first then each side then the top on both sides.
The roof shingles should be softened and flattened as the shingles tend to curl up in winter.
The shingles can be warmed up with a propane torch.
Make use of the flame carefully on the curled shingle edges.
Locate the leaking source and search for the damaged or missing shingles and make a list of the areas to be repaired.
Attach one end of the tarp to the length of a two by four board.
In the winter a dab of roofing cement or tar should be added to each shingle to bond them together until the tar strip is activated in warmer weather.
Sealing the shingle to the object can be accomlished with a roofing sealant available at menards lowes etc.
Cut the tarp or plastic sheeting to fit over the hole or leaking spot.
Small nail holes left behind from old vents satellite dish brackets or anything previously attached to the roof can allow water to enter and cause damage for years before leaking is noticed.
If a leak is difficult to find enlist a helper and go up on the roof with a garden hose.
The tar strip needs to be about 60f to activate.
Perhaps placing tube on furnace duct so air heats pre cut tube inside of home then climb up ladder and seal area keeping the sealant warm and easily caulk able.
However when it is not practical to climb up on the roof to fix a leak such as during the winter months you can repair a leaky roof temporarily from the inside if you can determine where the leak is occuring from the underside of your roof.